 3.1.1: Estimating Slope In Exercises 1 and 2, estimate the slope of the gr...
 3.1.2: Estimating Slope In Exercises 1 and 2, estimate the slope of the gr...
 3.1.3: Slopes of Secant Lines In Exercises 3 and 4, use the graph shown in...
 3.1.4: Slopes of Secant Lines In Exercises 3 and 4, use the graph shown in...
 3.1.5: Finding the Slope of a Tangent Line In Exercises 510, find the slop...
 3.1.6: Finding the Slope of a Tangent Line In Exercises 510, find the slop...
 3.1.7: Finding the Slope of a Tangent Line In Exercises 510, find the slop...
 3.1.8: Finding the Slope of a Tangent Line In Exercises 510, find the slop...
 3.1.9: Finding the Slope of a Tangent Line In Exercises 510, find the slop...
 3.1.10: Finding the Slope of a Tangent Line In Exercises 510, find the slop...
 3.1.11: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.12: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.13: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.14: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.15: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.16: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.17: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.18: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.19: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.20: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.21: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.22: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.23: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.24: Finding the Derivative by the Limit Process In Exercises 1124, find...
 3.1.25: Finding an Equation of a Tangent Line In Exercises 2532, (a) find a...
 3.1.26: Finding an Equation of a Tangent Line In Exercises 2532, (a) find a...
 3.1.27: Finding an Equation of a Tangent Line In Exercises 2532, (a) find a...
 3.1.28: Finding an Equation of a Tangent Line In Exercises 2532, (a) find a...
 3.1.29: Finding an Equation of a Tangent Line In Exercises 2532, (a) find a...
 3.1.30: Finding an Equation of a Tangent Line In Exercises 2532, (a) find a...
 3.1.31: Finding an Equation of a Tangent Line In Exercises 2532, (a) find a...
 3.1.32: Finding an Equation of a Tangent Line In Exercises 2532, (a) find a...
 3.1.33: Finding an Equation of a Tangent Line In Exercises 3338, find an eq...
 3.1.34: Finding an Equation of a Tangent Line In Exercises 3338, find an eq...
 3.1.35: Finding an Equation of a Tangent Line In Exercises 3338, find an eq...
 3.1.36: Finding an Equation of a Tangent Line In Exercises 3338, find an eq...
 3.1.37: Finding an Equation of a Tangent Line In Exercises 3338, find an eq...
 3.1.38: Finding an Equation of a Tangent Line In Exercises 3338, find an eq...
 3.1.39: Sketching a Derivative In Exercises 3944, sketch the graph of Expla...
 3.1.40: Sketching a Derivative In Exercises 3944, sketch the graph of Expla...
 3.1.41: Sketching a Derivative In Exercises 3944, sketch the graph of Expla...
 3.1.42: Sketching a Derivative In Exercises 3944, sketch the graph of Expla...
 3.1.43: Sketching a Derivative In Exercises 3944, sketch the graph of Expla...
 3.1.44: Sketching a Derivative In Exercises 3944, sketch the graph of Expla...
 3.1.45: Sketching a Graph Sketch a graph of a function whose derivative is ...
 3.1.46: Sketching a Graph Sketch a graph of a function whose derivative is ...
 3.1.47: Using a Tangent Line The tangent line to the graph of at the point ...
 3.1.48: Using a Tangent Line The tangent line to the graph of at the point ...
 3.1.49: Working Backwards In Exercises 4952, the limit represents for a fun...
 3.1.50: Working Backwards In Exercises 4952, the limit represents for a fun...
 3.1.51: Working Backwards In Exercises 4952, the limit represents for a fun...
 3.1.52: Working Backwards In Exercises 4952, the limit represents for a fun...
 3.1.53: Writing a Function Using Derivatives In Exercises 53 and 54, identi...
 3.1.54: Writing a Function Using Derivatives In Exercises 53 and 54, identi...
 3.1.55: Finding an Equation of a Tangent Line In Exercises 55 and 56, find ...
 3.1.56: Finding an Equation of a Tangent Line In Exercises 55 and 56, find ...
 3.1.57: Graphical Reasoning Use a graphing utility to graph each function a...
 3.1.58: HOW DO YOU SEE IT? The figure shows the graph of (a) (b) (c) What c...
 3.1.59: Graphical Reasoning Consider the function (a) Use a graphing utilit...
 3.1.60: Graphical Reasoning Consider the function (a) Use a graphing utilit...
 3.1.61: Graphical Reasoning In Exercises 61 and 62, use a graphing utility ...
 3.1.62: Graphical Reasoning In Exercises 61 and 62, use a graphing utility ...
 3.1.63: Approximating a Derivative In Exercises 63 and 64, evaluate and and...
 3.1.64: Approximating a Derivative In Exercises 63 and 64, evaluate and and...
 3.1.65: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.66: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.67: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.68: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.69: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.70: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.71: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.72: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.73: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.74: Using the Alternative Form of the Derivative In Exercises 6574, use...
 3.1.75: Determining Differentiability In Exercises 7580, describe the valu...
 3.1.76: Determining Differentiability In Exercises 7580, describe the valu...
 3.1.77: Determining Differentiability In Exercises 7580, describe the valu...
 3.1.78: Determining Differentiability In Exercises 7580, describe the valu...
 3.1.79: Determining Differentiability In Exercises 7580, describe the valu...
 3.1.80: Determining Differentiability In Exercises 7580, describe the valu...
 3.1.81: Graphical Reasoning In Exercises 8184, use a graphing utility to gr...
 3.1.82: Graphical Reasoning In Exercises 8184, use a graphing utility to gr...
 3.1.83: Graphical Reasoning In Exercises 8184, use a graphing utility to gr...
 3.1.84: Graphical Reasoning In Exercises 8184, use a graphing utility to gr...
 3.1.85: Determining Differentiability In Exercises 8588, find the derivativ...
 3.1.86: Determining Differentiability In Exercises 8588, find the derivativ...
 3.1.87: Determining Differentiability In Exercises 8588, find the derivativ...
 3.1.88: Determining Differentiability In Exercises 8588, find the derivativ...
 3.1.89: Determining Differentiability In Exercises 89 and 90, determine whe...
 3.1.90: Determining Differentiability In Exercises 89 and 90, determine whe...
 3.1.91: Greatest Integer Function and Differentiability Use a graphing util...
 3.1.92: Conjecture Consider the functions and (a) Graph and on the same set...
 3.1.93: The slope of the tangent line to the differentiable function at the...
 3.1.94: If a function is continuous at a point, then it is differentiable a...
 3.1.95: If a function has derivatives from both the right and the left at a...
 3.1.96: If a function is differentiable at a point, then it is continuous a...
 3.1.97: Differentiability and Continuity Let and Show that is continuous, b...
 3.1.98: Writing Use a graphing utility to graph the two functions and in th...
Solutions for Chapter 3.1: The Derivative and the Tangent Line Problem
Full solutions for Calculus: Early Transcendental Functions  6th Edition
ISBN: 9781285774770
Solutions for Chapter 3.1: The Derivative and the Tangent Line Problem
Get Full SolutionsChapter 3.1: The Derivative and the Tangent Line Problem includes 98 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. Since 98 problems in chapter 3.1: The Derivative and the Tangent Line Problem have been answered, more than 45305 students have viewed full stepbystep solutions from this chapter.

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Boxplot (or boxandwhisker plot)
A graph that displays a fivenumber summary

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Circle graph
A circular graphical display of categorical data

Complex conjugates
Complex numbers a + bi and a  bi

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

Data
Facts collected for statistical purposes (singular form is datum)

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

Focus, foci
See Ellipse, Hyperbola, Parabola.

Independent variable
Variable representing the domain value of a function (usually x).

Nonsingular matrix
A square matrix with nonzero determinant

nth root of unity
A complex number v such that vn = 1

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Real zeros
Zeros of a function that are real numbers.

Reciprocal function
The function ƒ(x) = 1x

Shrink of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal shrink) by the constant 1/c or all of the ycoordinates (vertical shrink) by the constant c, 0 < c < 1.

Transverse axis
The line segment whose endpoints are the vertices of a hyperbola.

Venn diagram
A visualization of the relationships among events within a sample space.

Ymin
The yvalue of the bottom of the viewing window.